Play Klondike's rules with Spider's stock: every card deals straight onto the tableau, no waste pile involved. This deal has been around since at least 1931.

Easthaven Solitaire plays like Klondike right up until the stock: instead of building a waste pile, each card deals straight onto a tableau pile, the way Spider's stock works. The tableau still builds down in alternating colors, and the foundations still climb up by suit. The game dates back to at least 1931.
If you enjoy Easthaven, the original Solitaire is the classic it borrows from, and the bigger Double Easthaven Solitaire and Triple Easthaven Solitaire push the same idea further.
If you run into anything odd or have an idea that would make the game better, please contact me.
Have a good time playing!
There are four foundation piles.
Any ace in the foundation may be transferred to any vacant pile.
A card can be added to a foundation pile only if it's one rank higher and the same suit as the pile's current top card, so the only card that fits on a 6 of hearts is a 7 of hearts.
The top card of each foundation can be moved back into play if another pile will accept it.
Seven tableau piles, three cards each. The top card is dealt face-up; the other two stay face-down.
A card can be added to a tableau pile only if it's one rank lower and the opposite color of the pile's current top card, so the only cards that fit on the 8 of diamonds are the 7 of spades and 7 of clubs.
Cards on the tableau that are not covered by another card are free to be played onto the foundation or any other tableau pile.
Any card can fill an empty slot in the tableau.
A run of cards in alternating colors, high to low, can move together from one tableau pile to another.
The stock holds the cards left over after the deal.
Click the stock once to deal a card face-up onto every tableau pile. That's your only pass through it, so use it when you need fresh cards across the board.